At LL accuracy in \(\log (s/|t|)\) , the four-gluon amplitude is real, and the antisymmetric octet \({\bf 8}_a\) 
is the only colour representation exchanged in the \(t\)  channel
to all orders in \(\alpha _s\)  [1]}, [2]},
\(\mathcal {M}_{4g}\big |_{LL} = \mathcal {M}^{[8_a]\, \text{fact}}_{4g}\big |_{LL} \,.\) 
